La conjecture de « symétrie miroir SYZ » prédit quʼune variété de Calabi–Yau X consiste en une famille de tores qui sont duaux dʼune famille de tores lagrangiennes spéciaux dans la variété miroir duale . Nous considérons ici une fibration de variétés abéliennes polarisées et nous en construisons la duale. De plus, nous montrons quʼelles sont équivalentes au niveau des catégories dérivées.
SYZ mirror conjecture predicts that a Calabi–Yau manifold X consists of a family of tori which are dual to a family of special Lagrangian tori on the mirror dual manifold . Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.
@article{CRMATH_2012__350_13-14_689_0, author = {Cristina Mart{\'\i}nez}, title = {Abelian fibrations and {SYZ} mirror conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {689--692}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.07.011}, language = {en}, }
Cristina Martínez. Abelian fibrations and SYZ mirror conjecture. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 689-692. doi : 10.1016/j.crma.2012.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.011/
[1] Les intersections complètes de nieveau de Hodge un, Invent. Math., Volume 15 (1972), pp. 237-250
[2] Mirror symmetry and elliptic curves, Texel Island, 1994 (Progr. Math.), Volume vol. 129, Birkhäuser, Boston, MA (1995), pp. 149-163
[3] Torus fibrations, gerbes, and duality (in Memoirs of the AMS) | arXiv
[4] Relative integral functors for singular fibrations and singular partners, J. Eur. Math. Soc. (JEMS), Volume 11 (2009), pp. 597-625
[5] Derived equivalences of Calabi–Yau fibrations | arXiv
Cité par Sources :
Commentaires - Politique
Fiberwise stable bundles on elliptic threefolds with relative Picard number one
Andrei Căldăraru
C. R. Math (2002)
Supersymmetric backgrounds from generalized Calabi–Yau manifolds
Mariana Graña; Ruben Minasian; Michela Petrini; ...
C. R. Phys (2004)